Ghayr 'amil: not governing what follows
غَيْر عَامِلghayr 'amil - non-governing
Ghayr amil describes a particle that does not govern what follows it in the same way.
Simple explanation
غَيْر عَامِل (ghayr 'amil) describes a particle that does not govern what follows it in the same way as an amil particle.